Ergodic distribution for a fuzzy inventory model of type (s, S) with gamma distributed demands

Abstract

In this study, a stochastic process (X(t)), which describes a fuzzy inventory model of type (s, S) is considered. Under some weak assumptions, the ergodic distribution of the process X(t) is expressed by a fuzzy renewal function U(x). Then, membership function of the fuzzy renewal function U(x) is obtained when the amount of demand has a Gamma distribution with fuzzy parameters. Finally, membership function and alpha cuts of fuzzy ergodic distribution of this process is derived by using extension principle of L. Zadeh. (C) 2012 Elsevier Ltd. All rights reserved.